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A prime number has exactly two factors.
A number has exactly three factors if and only if it is the square of a prime number.
Yes, a composite number is a number which has more than two factors, unlike prime numbers which have exactly two factors. The factors of 119 are 1,7,17 and 119 so it is composite (it has 4 factors).
16 (1, 2, 4, 8, and 16) and 81 (1, 3, 9, 27, and 81) each have exactly five factors.